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#1 2013-06-04 23:49:15

Stangerzv
Member
Registered: 2012-01-30
Posts: 173

My New Twin Prime Numbers Absolute Twin Primes

Consider this equation

Where n is an even number, Pi is the consecutive prime and Ps is the resulting prime.

Some of the primes

Let P1=2 and n=4

Ps={193, 227}

Let P1=2 and n=6

Ps={29989, 30071}


Let P1=3 and n=2

Ps={7, 23}


Let P1=3 and n=4

Ps={1129, 1181}

Let P1=5 and n=2

Ps={23, 47}

Let P1=5 and n=6

Ps={1616543, 1616687}

Last edited by Stangerzv (2013-06-04 23:50:25)

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#2 2013-06-05 02:07:17

Stangerzv
Member
Registered: 2012-01-30
Posts: 173

Re: My New Twin Prime Numbers Absolute Twin Primes

I think I could rearrange the equation to avoid negative prime. Below is the modified version.

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#3 2013-06-05 02:14:47

barbie19022002
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Registered: 2013-05-24
Posts: 1,314

Re: My New Twin Prime Numbers Absolute Twin Primes

did you make this equation yourself..?


Jake is Alice's father, Jake is the ________ of Alice's father?
Why is T called island letter?
think, think, think and don't get up with a solution...

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#4 2013-06-05 02:37:00

Stangerzv
Member
Registered: 2012-01-30
Posts: 173

Re: My New Twin Prime Numbers Absolute Twin Primes

Yep barbie19022002..I kinda like prime numbers and I do lots of thinking about them. Most of the prime numbers I listed here were not known to me before and this prime formula was developed this morning. I got to know about prime numbers through my formulation of sums of power for arithmetic progression. I got involved in prime numbers after trying to link my sums of power formulation with Riemann's zeta function. Sometimes, it is a frustration to know that someone else had found it but it is kool to find something without knowing it beforehand.

Last edited by Stangerzv (2013-06-05 03:07:39)

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#5 2013-06-05 02:52:09

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 84,748

Re: My New Twin Prime Numbers Absolute Twin Primes

Hi;

Seems that for P1 = 2 that they are very rare.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#6 2013-06-05 03:02:02

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,427

Re: My New Twin Prime Numbers Absolute Twin Primes

Here are some (unconfirmed):
P1 n
2, 4
2, 6
5, 4
5, 8


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#7 2013-06-05 03:04:27

Stangerzv
Member
Registered: 2012-01-30
Posts: 173

Re: My New Twin Prime Numbers Absolute Twin Primes

hi bobbym

There are three things that the prime has to match, a product, a sum and +- and when n becoming larger it would be harder to find the prime. This is what I believe and maybe a computational result would give a slightly different picture.

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#8 2013-06-05 03:14:16

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 84,748

Re: My New Twin Prime Numbers Absolute Twin Primes

There are no solutions with P1=2 and n < =1000 other than n = 4 and n = 6. These are already 3300 digit numbers!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#9 2013-06-05 03:15:28

Stangerzv
Member
Registered: 2012-01-30
Posts: 173

Re: My New Twin Prime Numbers Absolute Twin Primes

New update

P1=13 and n=2

Ps={191, 251}

P1=43 and n=2

Ps={1931, 2111}

Last edited by Stangerzv (2013-06-05 03:25:13)

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#10 2013-06-05 03:20:43

Stangerzv
Member
Registered: 2012-01-30
Posts: 173

Re: My New Twin Prime Numbers Absolute Twin Primes

Hi bobbym

I had a feeling it would be hard to find prime for n>6 for P1=2 and I quit looking for them and now knowing there is no prime for n up to 1000 it is just worthy not trying:)

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#11 2013-06-05 03:22:14

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 84,748

Re: My New Twin Prime Numbers Absolute Twin Primes

There are no solutions with P1=3 and n < = 1000 other than n = 2 and n = 4.

For P1=5 and n < = 1000 other than n = 2 and n = 6, I can find no others.

For P1=7 and n < = 1000, I can find no solutions.

For P1=11 and n < = 1000, I can find no solutions.

For P1=13 and n < = 1000 other than n = 2, I can find no others.

For P1=17 and n < = 1000, I can find no solutions.

For P1=19 and n < = 1000, I can find no solutions.

For P1=23 and n < = 1000, I can find no solutions.

For P1=29 and n < = 1000, I can find no solutions.

For P1=31 and n < = 1000, I can find no solutions.

For P1=37 and n < = 1000, I can find no solutions.

For P1=41 and n < = 1000, I can find no solutions.

For P1=43 and n < = 1000 other than n = 2, I can find no others.

For P1=47 and n < = 1000, I can find no solutions.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#12 2013-06-05 05:03:59

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,427

Re: My New Twin Prime Numbers Absolute Twin Primes

Let P1=2 and n=4

Ps={193, 227}

How are you getting this? It seems I have misread something...


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#13 2013-06-05 05:21:27

phrontister
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From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,844

Re: My New Twin Prime Numbers Absolute Twin Primes

Hi stefy,

P1 is the first prime in the sequence, and n is the number of primes in the sequence.

P1=2, n=4
2+3+5+7=17
2*3*5*7=210
210-17=193
210+17=227
Ps={193,227}

P1=3,n=2
3+5=8
3*5=15
15-8=7
15+8=23
Ps={7,23}

Last edited by phrontister (2013-06-05 05:27:52)


"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#14 2013-06-05 05:28:09

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,427

Re: My New Twin Prime Numbers Absolute Twin Primes

Ah, got it. Didn't subtract 1 in the upper summation bound.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#15 2013-06-05 06:37:17

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,844

Re: My New Twin Prime Numbers Absolute Twin Primes

Testing for n<=100, I found many solutions up to P1=50929, most of which are for n=2. There are some n=4, 6 and 8, and several loners: n=14, 22, 26 and 56.


"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#16 2013-06-05 06:49:41

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,427

Re: My New Twin Prime Numbers Absolute Twin Primes

Hi

For P1<=p_10000 there is nothing for 34<=n<=54 and 58<=n<=68.

Also did a search for (P1,n) pairs where P1 can go up to p_100000 and 34<=n<=68. 

Last edited by anonimnystefy (2013-06-05 10:22:38)


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#17 2013-06-05 12:34:34

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,844

Re: My New Twin Prime Numbers Absolute Twin Primes

The result with the highest n I've got so far is P=61001, n=154.

Backwards check (in M), where e1 and e2 are the two absolute +/- Ps elements:

Input: a = FactorInteger[(e1 + e2)/2]; {First[First[a]], Length[a]}
Output: {61001,154}

My code looks a bit clunky with the repeat "First[First", but it works and I don't know how to improve it.

Prime factor range is 61001 to 62761, which comprises 154 primes. 61001 and 62761 are the 6146th and 6299th primes (respectively), but I don't know how that information can be used.

Last edited by phrontister (2013-06-06 04:42:51)


"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#18 2013-06-06 16:57:23

Stangerzv
Member
Registered: 2012-01-30
Posts: 173

Re: My New Twin Prime Numbers Absolute Twin Primes

It seems there are plenty of these primes with an exception that most of them occur at smaller value of n.

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#19 2013-06-07 05:33:29

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,844

Re: My New Twin Prime Numbers Absolute Twin Primes

Yes, it's rarefied air up there for higher numbers.

I tried for P1=7, got to n=7350 with no result, and pulled the plug.


"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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